If \(\pi=3.14,\) then the value of \({\pi}^{2}\) is

(a)

9.8596

(b)

9.860

(c)

9.86

(d)

9.9

Which unit is used to measure size of a nucleus?

(a)

Angstrom

(b)

Micron

(c)

Nano

(d)

Fermi

A student measures the distance traversed in free fall of a body, initially at rest, in a given time, He uses this data to estimate g, the acceleration due to gravity, If the maximum percentage errors in measurement of the distance and the time are e₁ and e₂ respectively, the percentage error in the estimation of g is ______________.

(a)

e₂-e₁

(b)

e₁+2e₂

(c)

e₁+e₂

(d)

e₁-2e₂

In a vernier caliper, n divisions of vernier scale coincides with (n - 1) divisions of main scale. The least count of the instrument is ______________

(a)

\(\frac{1}{n}\)MSD

(b)

\({n\over n+1}\)MSD

(c)

\({ n+1\over n}\)MSD

(d)

\({ n+1\over n-1}\)MSD

If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant t is

(a)

1

(b)

2

(c)

4

(d)

0.5

If \(\bar A\) and \(\bar B\) denotes the sides of a parallelogram whose area is \(\frac{1}{1}\left| A \right|\left| B \right|\) the angle between \(\bar A\) and \(\bar B\) is _______________

(a)

60°

(b)

45°

(c)

30°

(d)

90°

If the length of the second hand in a stop clock is 3cm. The angular velocity and linear velocity of the tip is _______________

(a)

0.2047 rad/s; 0.0314 ms^-1

(b)

0.2547 rad/s; 0.314 ms^-1

(c)

0.1472 rad/s; 0.06314 ms^-1

(d)

0.1047 rad/s; 0.00314 ms^-1

A butterfly and stone (mass of later is greater than earlier) is moving with same velocity. Momentum of the stone is____________ than the momentum of butterfly.

(a)

equal

(b)

greater

(c)

lesser

(d)

lesser (or) equal to

If the coordinate axes (x, y, z) are drawn in anticlockwise direction then the co-ordinate system is known as ______________.

(a)

Cartesian coordinate system

(b)

right-handed coordinate system

(c)

left-handed coordinate system

(d)

cylindrical coordinate system

One radian is equal to _______________.

(a)

\(\frac{\pi}{180}\) degree

(b)

60^o

(c)

57.295^o

(d)

53.925^o

An object is dropped from rest. Its v - t graph is ______________.

(a)

(b)

(c)

(d)

Which of the following graph represents the equation y = mx?

(a)

(b)

(c)

(d)

A ball is thrown vertically upward. It is a speed of 10 m/s. When it has reached one half of its maximum height. How high does the ball rise? (g = 10 ms^-2)

(a)

7 m

(b)

10 m

(c)

12 m

Momentum is closely related to _______________.

(a)

Force

(b)

Impulse

(c)

Velocity

(d)

K.E

A rocket with a lift off mass 2.5 \(\times\) 10⁴ kg is blast upward with an initial acceleration of 5m/s². Then the initial thrust of the blast is ______________.

(a)

1.75 \(\times\)10⁵N

(b)

7 \(\times\)10⁵N

(c)

37.5\(\times\) 10⁵N

(d)

14 \(\times\)10⁵N

How many degrees make a one newton?

(a)

10² dyne

(b)

20² dyne

(c)

10⁵ dyne

(d)

20⁵ dyne

Which law gives a method of measuring force?

(a)

Newton's first law of motion

(b)

Newton's second law of motion

(c)

Newton's third law of motion

(d)

None

Two blocks m₁ = 5gm and m₂ = 10gm are hung vertically over a light frictionless pulley as shown here. What is the acceleration of the masses when they are left free? (where g is acceleration due to gravity)

(a)

\(\frac { g }{ 3 } \).

(b)

\(\frac { g }{ 2 } \)

(c)

g

(d)

\(\frac { g }{ 5 } \)

According to the conservation of linear momentum ________________.

(a)

momentum before impact = momentum after impact

(b)

momentum before impact > momentum after impact

(c)

momemtum before impact < momentum after impact

(d)

momentum before impact is inversely proportional to momentum after impact

Which of the following is the dimension of coefficient of friction?

(a)

[MLT^-2]

(b)

[M⁰L⁰T⁰]

(c)

[M²LT^-2]

(d)

[M²LT]

A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change ________________.

(a)

1 : 4

(b)

\(\frac { 1 }{ 4 } :1\)

(c)

2:1

(d)

4:1

A body of mass 'm' rests on a horizontal plane. It the angle of friction is ፀ, the least force required to move the body along the plane is (g = acceleration due to gravity).

(a)

mg sinፀ

(b)

mg cosፀ

(c)

mg tanፀ

(d)

mg secፀ

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius \(\frac { r }{ 3 } \) and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier. stone when they experience same centripetal forces. The value of n is _______________.

(a)

4

(b)

1

(c)

2

(d)

3

A body of mass M hits normally a rigid wall with velocity V and bounces back with the same velocity. The impulse experienced by the body is ______________.

(a)

MV

(b)

1.5 MV

(c)

2MV

(d)

zero

A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength is 75% of the weight of the monkey, the minimum acceleration with which monkey can slide down without branch is ______________

(a)

g

(b)

\(\frac { 3g }{ 4 } \)

(c)

\(\frac { g }{ 4 } \)

(d)

\(\frac { g }{ 2 } \)